What is the molecular mass of a substance X if 1.00 L of a solution containing 4, 5 g of X has an osmolality of 0.337 mmHg the 30° C?
∏ = MRT = [moles/Vol(Liters)]RT => moles = (∏·Vol(Liters)/RT) = mass(gms)/Mol Wt
Solve for Mol Wt = [mass(gms)·R·T/∏·Vol(Liters)]
Mass = 4.5-gms
R = (0.08206 L-Atm/mole-K)
T = (30 + 273)K = 303K
∏ = (0.337/760)Atm = 4.4 x 10^-4 Atm
Vol(Liters) = 1.00 Liters
Substitute into Mol Wt Equation above => 252,000 g/mol
Thanks :)
To find the molecular mass of substance X, we need to use the equation:
Osmolality (m) = (molar mass (g/mol) * number of moles) / volume (L)
First, we need to convert the given osmolality from mmHg to atm:
0.337 mmHg = 0.337 mmHg * (1 atm / 760 mmHg) ≈ 0.0004447 atm
Next, we can rearrange the equation to solve for the molar mass:
Molar mass (g/mol) = (osmolality (m) * volume (L)) / number of moles
Since we are given the volume of the solution (1.00 L) and the mass of substance X (4.5 g), we need to determine the number of moles of substance X.
Number of moles = mass (g) / molar mass (g/mol)
Since we do not know the molar mass yet, we can temporarily use a variable, M, to represent it:
Number of moles = 4.5 g / M
Now, we can substitute the values into the rearranged equation:
Molar mass (g/mol) = (0.0004447 atm * 1.00 L) / (4.5 g / M)
Simplifying further:
Molar mass (g/mol) = 0.0004447 atm * 1.00 L * M / 4.5 g
Finally, we can calculate the molar mass of substance X by substituting the given values:
Molar mass (g/mol) = 0.0004447 atm * 1.00 L * M / 4.5 g
Molar mass (g/mol) ≈ 9.8833 M / g
Therefore, the molecular mass of substance X is approximately 9.8833 g/mol.